March 16th, 2010, 04:58 AM  #1 
Newbie Joined: Mar 2010 Posts: 7 Thanks: 0  Twin primes
If n and n+2 are twin primes, there are other two couples of twin primes (l, l+2, m and m+2) so that: n = l+m+1 Is it through? 
March 16th, 2010, 06:08 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Twin primes Quote:
First cut: "If n is a twin prime, there exist twin primes l and m with n = l + m + 1." This is false; take n = 3. Second cut: "Do there exist twin primes l, m, n with n = l + m + 1?" This is true; take (l, m, n) = (5, 5, 11). Third cut: "There exist infinitely many twin primes n such that n = l + m + 1, with l and m twin primes." This cannot be proven with present techniques; it is stronger than the twin prime conjecture. Can you clarify what you meant, if it wasn't one of these guesses?  
March 16th, 2010, 11:43 PM  #3 
Newbie Joined: Mar 2010 Posts: 7 Thanks: 0  Re: Twin primes
Please, let consider the question in a different way. 1 3 5 11 17 29 41 59 … 227 ... 2 4 6 12 18 30 42 60 … 228 ... 3 5 7 13 19 31 43 61 … 229 ... Is it through that each number in the central line can be written as a sum of other two numbers of the same line? e.g. 30 = 18 + 12 so that 29 = 17 + 11 + 1 and 31 = 19 + 13 – 1 228 = 198 + 30 so that 227 = 197 + 29 + 1 and 229 = 199 + 31  1 
March 17th, 2010, 04:46 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Twin primes
Are even numbers the sum of two odd numbers? Yes. But I don't know if that's what you intended.

March 17th, 2010, 05:37 AM  #5 
Newbie Joined: Mar 2010 Posts: 7 Thanks: 0  Re: Twin primes
Each even number is the average of twin prime (e.g. 12 = (11+13)/2) Then, 1,3 > 2, 3,5 > 4, 5,7>6....,17,19>18,...,59,61>60,.... We have then a sequence, 2, 4, 6, 12, 18, 30,...,60,... My question is if is it through that each number of the sequence can be written as the sum of other two numbers of the same sequence. 
March 17th, 2010, 06:41 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Twin primes Quote:
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March 25th, 2010, 01:19 AM  #7 
Newbie Joined: Mar 2010 Posts: 7 Thanks: 0  Re: Twin primes
If all elements of A167777 can be written as the sum of two members of A167777,it means that each twin prime is a function of two other twin primes.

March 25th, 2010, 10:18 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Twin primes Quote:
if m = 3, the first twin prime greater than n; if m = 5, the first twin prime less than n, or 0 if none exists; otherwise, 0. } For every twin prime p (here meaning members of A001097), there exist two different twin primes q and r such that p = f(q, r): 3 = f(5, 5) 5 = f(3, 3) 7 = f(3, 5) 11 = f(3, 7) . . .  

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